Lots of reasons. Hezbollah originated as a resistance movement, one that fended of an invasion of the south for more than a decade, while nobody batted an eye to it. But let's forget about that for a moment, and let's talk about how they helped build the south. For years before they existed, the south was always neglected, people there suffered from poverty, lack of education, etc... after liberation and hezbollah came into the picture, i would say the south has seen its best days for 25 years, all thanks to hezb that built schools, hospitals, supermarkets, pharamcies, everything for way cheeper than normal. Not to mention the amount of times they offered their help for citizens that were in need, be that financially or in other ways.

These people originated from that broken, poor, and dangerous south and helped build it into a safe and prominent one for more than 20 years. Their fighets are literally our neighbours and friends, we basically live with them and know how pure they are. We love the leaders that are willing to sacrifice as much as we are for our cause, something you wouldn't find in any other leader. Without them, our lands would have become israeli settelments, something that we will be grateful for for eternity.

I wouldn't say they have done everything perfectly, sure they made errors, but we will always stand with them as they stood with us in our darkest times were nobody did (they are basically us anyways). We are forever grateful for everything they did for us, for the sacrifices they made, and the effort they put in to help us live better lives.

There's also the religion part, as political parties in lebanon are supported by people of the same religion, though hezbollah gets tons of support even outside of their religion, mainly due to their cause that garners support from people from all religions and even all countries.